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Potential dominance of oscillating crescent waves in finite width tanks

American Institute of Physics
Publication Date
  • Recently
  • It Has Been Proposed That The Emergence Of Previously Observed Oscillating Crescent Water Wave Patte
  • Created By Class Ii (Three-Dimensional) Instabilities Which Are In Principle Not Dominant
  • Could In Fact Be Explained As An Artifact Of A Finite Width Tank
  • Combined With A Suppression Of The Class I (Benjamin-Feir) Instability
  • Within This Context
  • We Investigate Quantitatively The Dominance Of Class Ii Deep Water Wave Instabilities For Particular
  • And It Is Shown That The Regions Where Non-Phase-Locked (Oscillating) Crescent Wave Patterns Are Loc
  • Particularly For Low To Moderate Wave Steepness
  • This Is An Important Realization For Both Experimentalists And Numerical Modelers Currently Studying


Potential dominance of oscillating crescent waves in finite width tanks David R. Fuhrmana! and Per A. Madsenb! Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark sReceived 9 September 2004; accepted 16 November 2004; published online 2 February 2005d Recently, it has been proposed that the emergence of previously observed oscillating crescent water wave patterns, created by class II sthree-dimensionald instabilities which are in principle not dominant, could in fact be explained as an artifact of a finite width tank, combined with a suppression of the class I sBenjamin–Feird instability. Within this context, we investigate quantitatively the dominance of class II deep water wave instabilities for particular transversal wavenumbers, and it is shown that the regions where non-phase-locked soscillatingd crescent wave patterns are locally dominant is surprisingly large, particularly for low to moderate wave steepness. This is an important realization for both experimentalists and numerical modelers currently studying these phenomena. © 2005 American Institute of Physics. fDOI: 10.1063/1.1852291g The observation by Collard and Caulliez1 of oscillating crescent waves in their physical experiments has puzzled sci- entists, as these are due to what is, in principle, a nondomi- nant class II sRef. 2d wave instability sthe dominant instabil- ity corresponds to the phase-locked crescents observed, e.g., by Su et al.3d. Indeed, Collard and Caulliez state that the emergence of their oscillating crescents could not be ex- plained using existing theories. Recently, however, Fuhrman et al.4 have demonstrated that the emergence of oscillating crescent wave patterns, very similar to those observed by Collard and Caulliez, could in fact be explained directly from the stability analysis of McLean,2 when effects from a finite width tank were taken into account, combined with a suppression of the class I instability. They discuss a single example, fitting precis

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